Symmetries of parabolic contact structures
arXiv:1003.5443 · doi:10.1016/j.geomphys.2010.06.013
Abstract
We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion--free and some types of them have to be locally flat. We prove that each symmetry given at a point with non--zero harmonic curvature is involutive. Finally we give restrictions on number of different symmetries which can exist at such a point.
19 pages